Inverse in a group ring

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I have seen the question that is similar but I do not understand the answer whatsoever.

I have a group ring $R:=\mathbb{Q}S_3$ and want to find inverse of

$x=e+(2\,3) -(1\,3\,2)$

So is my $x^{-1}$ of the form

$e+ (a \, b)+(a\,c)+(b\,c)+(a\,b\,c)+(a\,c\,b)$

Or? And if so, how on earth do I solve using $xx^{-1}=e$?